Question

The mole fraction of carbon dioxide (xco2) in water is 0.25. determine the molarity of co2. (assume the density of the solution is 1.0 g/ml.)

Answer 1

Answer: Molarity of $CO_2$ is 18.51 mol/L.

Explanation: We are given the mole fraction of $CO_2$ which is 0.25.

The total number of moles = 1

Mole fraction of $H_2O=1-0.25=0.75$

Formula for Mole fraction is given by:

$\text{Mole fraction}=\frac{\text{Number of moles}}{\text{Total number of moles}}$

Moles of $CO_2=0.25\times 1=0.25$  (Solute)

Moles of $H_2O=0.75\times 1=0.75$   (Solvent)

The mass can be calculated using the formula:

$Moles=\frac{\text{Given mass}}{\text{Molar mass}}$

For $H_2O$

Molar mass = 18 g/mol

Putting the values in above equation, we get

$0.75=\frac{\text{Given mass}}{18}$

Mass of $H_2O$ = 13.5 g

Density of water = 1.0 g/mL (Given)

Volume of water is calculated by:

$Density=\frac{mass}{Volume}$

$1.0=\frac{13.5}{Volume}\\V=13.5mL$

Molarity is calculate by:

$Molarity=\frac{\text{Number of moles of solute}\times 1000}{\text{Volume of solvent (in mL)}}$

$Molarity=\frac{0.25\times 1000}{13.5}=18.51mol/L$

Answer 2

Let us assume that there is 1 mole of the solution present. The mass becomes:

Mass = fraction of carbon dioxide * Mr of carbon dioxide + fraction of water * Mr of water

Mass = 0.25*44 + 0.75*18

Mass = 24.5 grams

Now, we determine the volume of the solution using:

Volume = mass / density

Volume = 24.5/1 = 24.5 mL

The molarity of a solution is:

Molarity = moles / liter
Molarity = 0.25 / 0.0245

Molarity = 10.2 M